Torsional vibration control of a shaft through active constrained layer damping treatments

This paper proposes a hybrid damping design to control torsional vibration of a shaft with a circular cross section through use of actively constrained layer (ACL) damping treatments proposed by Bat (1993) and Shen (1993, 1994a). The ACL damping treatment consists of a piezoelectric constraining layer and a viscoelastic shear layer wrapping around the shaft in the form of alpha helix. In addition, the angular displacement of the shaft is fed back to regulate the helical motion of the piezoelectric constraining layer The equation of motion of this design is derived, and its stability and controllability are discussed. Finally, numerical examples show that this ACL design can reduce torsional vibration of a shaft. A sensitivity analysis shows that ACL is most effective in suppressing those modes with significant torsional vibration response. Stability, in general, is not a critical factor in designing ACL systems because the piezoelectric strain of the constraining layer at the threshold of instability is too large to occur.